LOHIER, Circuit Judge:

Defendant-appellant Troy Culbertson appeals from a judgment of conviction entered in the United States District Court for the Eastern District of New York (Johnson, J.). Culbertson's conviction arose from his plea of guilty to four counts of an eleven-count superseding indictment, including a count for conspiracy to import 100 grams or more of heroin and five kilograms or more of cocaine, in violation of 21 U.S.C. §§ 963, 960(b)(1)(B)(ii), and 960(b)(2)(A), and 18 U.S.C. §§ 3551 et seq. The District Court sentenced him principally to a term of imprisonment of 120 months. Culbertson is currently serving his sentence.

On appeal, Culbertson makes two arguments. First, he argues that the District Court erred in accepting his guilty plea without first "determin[ing] that there [was] a factual basis for the plea." Fed. R.Crim.P. 11(b)(3). In particular, Culbertson contends that the District Court lacked a factual basis to accept his plea to the statutorily prescribed drug quantity of five kilograms or more of cocaine, which triggers a mandatory minimum sentence of ten years' imprisonment, because he insisted during the plea that he was responsible for only three kilograms of cocaine. Second, Culbertson argues that he was deprived of his Sixth Amendment right to counsel because the District Court denied his motion to substitute counsel and his "standby counsel" during the plea rendered ineffective assistance.

As we conclude that Culbertson's plea failed to satisfy the requirements of Rule 11(b)(3) of the Federal Rules of Criminal Procedure, we do not resolve Culbertson's second basis for challenging his conviction. We remand with instructions to the District Court to vacate the judgment of conviction.

BACKGROUND

1. Investigation and Arrest

In 2007, federal agents started investigating an international narcotics trafficking ring that imported heroin and cocaine from Trinidad to cities in the United States. The agents learned of Culbertson's involvement in that ring on January 9, 2008, when his girlfriend, Patricia Lancaster, arrived at John F. Kennedy International Airport from Trinidad. Customs officials discovered that Lancaster's suitcase contained just over ten kilograms (10,369 grams) of cocaine and about 909 grams of heroin. Lancaster was arrested and immediately started to cooperate. She explained that Culbertson and another man had offered her $5,000 to smuggle narcotics from Trinidad to New York and had assured her that two other individuals would meet her at the airport to retrieve the drugs.

While the agents were questioning Lancaster, Culbertson called the airport's Customs and Border Protection office inquiring about Lancaster's whereabouts. Under the agents' supervision, Lancaster called Culbertson and asked that he pick her up, as no one had met her at the airport. Culbertson responded that he would meet Lancaster at the airport because her luggage contained a "product" that needed to be retrieved. The agents arrested Culbertson as soon as he arrived.

2. The Charges

In March 2008, a grand jury indicted Culbertson on four counts as part of a broader, superseding indictment in which Lancaster and others were also named as defendants. The indictment charged Culbertson with (1) conspiring to import and importing five kilograms or more of cocaine and 100 grams or more of heroin, principally in violation of 21 U.S.C. §§ 963, 960(b)(1)(B)(ii), and 960(b)(2)(A) (Counts One and Five); and (2) conspiring and attempting to possess with intent to distribute the same amount of cocaine and heroin, principally in violation of 21 U.S.C. §§ 846, 841(b)(1)(A)(ii)(II), and 841(b)(1)(B)(i) (Counts Two and Seven).

3. Pre-Plea Proceedings

At a pretrial conference on May 15, 2008, Allen Lashley, Culbertson's fourth appointed attorney of record,1 reported that he and Culbertson had argued over his refusal to file a "frivolous motion" and that Culbertson had fired him. Culbertson complained: "I can't get my lawyer to do anything for me, and I don't know the law." The District Court responded as follows:

When Culbertson protested that he did not want to proceed pro se and that he "need[ed] help," the District Court responded that he was "on [his] own," but also told him, "If you need help and you want to call Mr. Lashley, you are free to do it." In the ensuing months, Lashley continued to appear at pretrial conferences as Culbertson's standby counsel. Culbertson later filed a pro se "Motion for Appointment of Counsel," in which he asserted that each of his lawyers had been unfit and that he was incapable of representing himself. The District Court denied the motion, referring to its broad discretion to decline to appoint new counsel and noting that an indigent defendant is not entitled to his counsel of choice.

The District Court set a trial date of February 9, 2009. During a conference only a few weeks prior to trial, after reviewing Culbertson's history with prior counsel, the court observed that Culbertson was set to proceed pro se at trial, and sought to clarify Lashley's role as "standby counsel":

Culbertson responded, "I don't want to go pro se. I don't want Mr. Lashley because he's not doing anything for me," and "I'm asking the court for a lawyer." The District Court confirmed that Lashley would serve as standby counsel at trial if Culbertson wished, but that Culbertson was otherwise "on [his] own." Again, Culbertson protested that he did not want to proceed pro se because he did not "know how to do a trial from beginning to end."

4. The Plea Proceeding

On January 21, 2009, the District Court held another conference, which culminated in Culbertson's guilty plea. At the start of the conference, the court re-emphasized that Culbertson's options were to proceed pro se or accept Lashley as his attorney. Lashley advised the Court that he had been unsuccessful in "tr[ying] to obtain a plea bargain to Mr. Culbertson's satisfaction." Lashley explained, "I advised [Culbertson] he doesn't have to plead to the plea agreement, he could plead to the indictment, and then at the time of sentence or before sentence we can bring up all of the arguments that he has concerning what type of sentence he should get from the Court." The District Court briefly adjourned the conference to permit Culbertson, Lashley, and the Government to continue discussing a possible disposition.

When the parties returned, Lashley stated that Culbertson wished to plead guilty to all the counts against him in the superseding indictment, although no formal plea agreement had been reached and the Government had not delivered a letter pursuant to United States v. Pimentel, 932 F.2d 1029 (2d Cir.1991). Before proceeding with the plea, the Government confirmed that Culbertson had reserved his rights to an evidentiary hearing regarding drug quantity.

During the plea proceeding, the District Court verified that Culbertson was competent, that he had discussed the charges against him with his "legal advisor," Lashley, and that he understood Lashley's advice regarding the charges. Culbertson said that he understood that he faced a maximum sentence of life imprisonment and a minimum sentence of ten years. The Government then proffered that its proof against Culbertson consisted principally of an audio recording of Culbertson speaking by phone with Lancaster about importing the drugs in her suitcase, which included over one hundred grams of heroin and over five kilograms of cocaine. Culbertson allocuted that he had recruited Lancaster to bring narcotics into the United States from Trinidad. After the allocution, the District Court asked Culbertson whether he knew that Lancaster was "coming into this country with narcotics," and Culbertson responded, "Yes. We made an agreement for three kilos of cocaine." The court then asked the Government if it had any additional questions, which prompted the following colloquy:

After describing the charges against Culbertson without further mentioning drug quantity or advising Culbertson of the elements of each charge, the District Court accepted Culbertson's plea.

5. Post-Plea Proceedings and Sentencing

Prior to his plea, Culbertson had requested a Fatico hearing to determine the amount of cocaine for which he was responsible. After the plea, the Government responded that, for sentencing purposes, it would rely solely on the five-kilogram minimum weight necessary to trigger the ten-year mandatory minimum sentence, rendering a Fatico hearing unnecessary. The District Court denied the request for a Fatico hearing as "moot in light of the government's response."

Before sentencing, Culbertson filed a pro se motion to withdraw his guilty plea, arguing, among other things, that he had entered the plea under pressure and that he had been unconstitutionally denied the assistance of counsel during his plea proceeding. Culbertson also filed a pro se motion requesting that the District Court impose a sentence below the ten-year statutory minimum because he was responsible for only three, not five, kilograms of cocaine. Under the Controlled Substances Act, a plea to three kilograms of cocaine would have triggered only a five-year mandatory minimum sentence.

At Culbertson's sentencing, the District Court accepted the presentence report's calculation that Culbertson's Guidelines range was 57 to 71 months.2 However, having determined that Culbertson was subject to a ten-year mandatory minimum sentence because his offense involved at least five kilograms of cocaine, the court concluded that it was without authority to impose a lesser sentence. Culbertson again insisted that he should be sentenced based on three rather than five kilograms of cocaine because he had pleaded guilty to "three kilos" and had sought a Fatico hearing. The court responded, "Whatever count that you pled to calls for a mandatory minimum." It then sentenced Culbertson to 120 months' imprisonment.

This appeal followed.

DISCUSSION

1. The Factual Basis for the Guilty Plea

Culbertson argues that the District Court violated Federal Rule of Criminal Procedure 11(b)(3) by accepting his guilty plea without an adequate factual basis. He contends that he consistently and explicitly challenged the statutorily prescribed drug quantity of five kilograms or more of cocaine and maintained that he was responsible for only three kilograms.

a. Standard of Review

"We review for . . . abuse of discretion a district court's decision that a defendant's factual admissions support conviction on the charge to which he has pleaded guilty." United States v. Adams, 448 F.3d 492, 498 (2d Cir.2006). In the wake of Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000), however, we recognize that "a defendant cannot be convicted on an aggravated [drug] offense unless the statutory drug quantity is proved to a jury or admitted by the defendant." United States v. Gonzalez, 420 F.3d 111, 124 (2d Cir.2005).

b. Factual Basis for Drug Quantity

We have previously held that in order to provide a factual basis for a plea to a drug conspiracy charge under 21 U.S.C. § 841(b)(1)(A), an allocution must establish that the "drug type and quantity were at least reasonably foreseeable to the co-conspirator defendant." Adams, 448 F.3d at 499. In United States v. Gonzalez, for example, we reviewed the adequacy of a plea allocution regarding drug quantity under Rule 11(b)(3) by a defendant who was charged under § 841(b)(1)(A) with conspiring to distribute 50 grams or more of crack cocaine, an amount that carried a twenty-year mandatory minimum sentence. Gonzalez, 420 F.3d at 119, 121, 133. Gonzalez, the defendant, "specifically declined to plead guilty to conspiring to distribute the charged fifty grams or more of crack, explaining. . . that he had never intended to sell the informant a kilogram of real crack," but had intended to sell only a counterfeit substance. Id. at 117. We held "that Gonzalez's failure to admit— indeed, his explicit challenge to—the statutorily prescribed quantity meant that his plea did not provide the court with an adequate factual basis to enter judgment against him on the charged crime," and we remanded to the district court with instructions to vacate the judgment of conviction. Id. at 133-34.

In United States v. Adams, we considered another Rule 11(b)(3) challenge to a plea by a defendant who allocuted that he had participated in a scheme to "transport eighty-five to ninety pounds of marijuana," but who was ultimately convicted of conspiring to transport five kilograms or more of cocaine. 448 F.3d at 495. After the allocution, the Government clarified that Adams, the defendant, had stipulated that he would be sentenced based on at least five kilograms of cocaine. Alerted to the inconsistency, the court asked Adams two questions before accepting his plea: (1) "whether he realized that he had agreed to sentencing for a cocaine conspiracy," and (2) "[a]lthough [he] didn't know that the load was coke at the time," whether "[he] did know that it was a drug and it was illegal." Id. at 496. Adams answered both questions "in the affirmative." Id. We nevertheless concluded that there was an insufficient factual basis for the plea and that the district court had "failed to elicit an admission that [the defendant] actually knew he was conspiring to distribute at least five kilograms of cocaine," because Adams had "insisted that he knew of and agreed to only a marijuana conspiracy." Id. at 499.

Our holdings in Gonzalez and Adams extend to Culbertson's conviction under 21 U.S.C. § 963, which, like 21 U.S.C. § 846, requires a showing that the defendant "knew of his co-conspirator's illicit activities or [that] the activities were reasonably foreseeable by him." United States v. Jackson, 335 F.3d 170, 181 (2d Cir.2003). Like the defendants in those cases, Culbertson "specifically declined" to plead guilty to a drug quantity involving more than five kilograms, Gonzalez, 420 F.3d at 117, and "insisted that he knew of and agreed to" a conspiracy to transport only three kilograms, Adams, 448 F.3d at 499. When asked to describe the conduct that led him to believe he was guilty, Culbertson responded that he had agreed with Lancaster to transport three kilograms of cocaine. Immediately after the Government proffered that Lancaster had in fact transported five kilograms of cocaine, the District Court referred to "three kilos of coke," a reference that prompted Culbertson to repeat that he was responsible for only three kilograms of cocaine, and to point out that Lancaster had pleaded guilty to only three kilograms. Culbertson's persistent disavowal of responsibility for any amount in excess of three kilograms of cocaine compels us to conclude that the District Court lacked a factual basis for his plea.

The Government contends that its proffer of proof during Culbertson's plea provided a sufficient factual basis under Rule 11. We disagree. It is true that, to establish the factual basis required by Rule 11, the district court may rely on representations of "the defendant, of the attorneys for the government and the defense, [or] of the presentence report when one is available," and indeed may use "whatever means is appropriate in a specific case." United States v. Maher, 108 F.3d 1513, 1524 (2d Cir.1997) (quoting Fed. R.Crim.P. 11, Advisory Committee Note (1974)). But it is error for the court to find that a factual basis exists when the defendant actively contests a fact constituting an element of the offense in the absence of circumstances warranting the conclusion that the defendant's protestations are "unworthy of belief."3 Godwin v. United States, 687 F.2d 585, 590 (2d Cir. 1982); see also Montgomery v. United States, 853 F.2d 83, 85-86 (2d Cir.1988) (vacating guilty plea where defendant admitted only to conspiring with government agents and informants, but "flatly refused to admit" conspiring with the person named in the indictment); cf. United States v. Navedo, 516 F.2d 293, 297-98 (2d Cir. 1975) (upholding lower court's rejection of a guilty plea where the defendant denied knowledge of, and intent to participate in, a drug conspiracy). Under Rule 11, moreover, the court must "assure itself. . . that the conduct to which the defendant admits is in fact an offense under the statutory provision under which he is pleading guilty." Maher, 108 F.3d at 1524. In doing so, it is "essential . . . that the court determine by some means that the defendant actually understands the nature of the charges." Id. at 1521.4

Again, far from admitting that he knew or reasonably could have foreseen that Lancaster was transporting over five kilograms of cocaine, or that the Government could prove the foreseeability of this amount, Culbertson affirmatively disputed this essential element of the charged crime. In addition, the District Court's mistaken reference to "three kilos of coke" after the Government's proffer served to muddle rather than clarify the quantity to which Culbertson was pleading guilty.

Relying on United States v. Andino, 627 F.3d 41 (2d Cir.2010), the Government urges us to affirm Culbertson's conviction on the ground that he personally and directly participated in the drug transaction underlying the conspiracy charges against him, and that under these circumstances the Government need not prove knowledge or foreseeability. Id. at 47. Accordingly, the Government submits, Culbertson should be held responsible for the actual amount of cocaine found in Lancaster's suitcase—an amount that it claims he never disputed. This argument is unpersuasive for two reasons.

First, Culbertson appears to have challenged the actual amount of cocaine in Lancaster's suitcase, as well as his knowledge of that amount. Culbertson never acknowledged that Lancaster was found with five kilograms of cocaine and, indeed, insisted that Lancaster's plea reflected that she had only three kilograms of cocaine. Second, the record belies the Government's contention that Culbertson personally and directly participated in the drug transaction. In Andino, we held that the Government need not "prove scienter as to drug type or quantity when a defendant personally and directly participates in a drug transaction underlying a conspiracy charge." 627 F.3d at 47. We concluded that a defendant who retrieved a package containing drugs addressed to him and transported it to another building had personally and directly participated in that transaction and could be sentenced based on the type and quantity of drugs in the package, even if those were not reasonably foreseeable to him. Id. We were careful to contrast Andino's case, however, with cases such as Adams, in which the defendant merely "recruited another individual to transport drugs on his behalf." Id. at 47 n. 3 (citing Adams, 448 F.3d at 495).

Here, Culbertson recruited Lancaster to transport cocaine from Trinidad, but there is no evidence that he actually handled the cocaine or was involved beyond the recruitment. Moreover, the District Court found that Culbertson was entitled to a significant downward adjustment under the Sentencing Guidelines for playing a "minimal role" in the offense. This adjustment is available only to "a defendant who plays a part in committing the offense that makes him substantially less culpable than the average participant." U.S.S.G. § 3B1.2(a) (commentary n. 3 (A)). That finding indicates that Culbertson's role was far from direct.

c. Harmless Error

Having determined that the District Court erred in accepting Culbertson's plea without a sufficient factual basis, we turn to whether the "variance from the requirements of" Rule 11 constituted "harmless error" or instead "affect[ed] substantial rights." Fed.R.Crim.P. 11(h).

"[T]he kinds of Rule 11 violations that can properly be considered harmless error are `fairly limited.'" Maher, 108 F.3d at 1521 (quoting Fed.R.Crim.P. 11, Advisory Committee Note (1983) (Rule 11(h))). In Gonzalez, we described drug quantity as "presumptively significant" because of its "potential impact on any term of incarceration, both in terms of the statutory minimum and the Sentencing Guidelines." 420 F.3d at 132, 133. We explained that drug quantity is particularly significant when "[t]he record plainly demonstrates that" it is "the only fact [the defendant] wished to contest with respect to the charged conspiracy." Id. at 132-33. After Gonzalez, we made the following pronouncement:

Adams, 448 F.3d at 502 (quoting Godwin, 687 F.2d at 591 (internal citations omitted)).

Culbertson clearly disputed the Government's proffer regarding drug quantity. As evidenced by his request for a Fatico hearing, he also appears to have understood the impact the issue of drug quantity would have at his sentencing. In view of Culbertson's explicit challenge to this element of the offense, and its effect on his term of incarceration, we conclude that the District Court's error in accepting Culbertson's plea was not harmless. We therefore remand to the District Court with instructions to vacate the judgment of conviction.5

2. Additional Arguments

Although Culbertson's conviction must be vacated because of the lack of a factual basis for his plea, in order to avoid problems on remand we also address his argument that the district court erred by requiring him to proceed pro se after disagreements with his fourth court-appointed counsel.

While the Sixth Amendment guarantees a right to competent court-appointed counsel in criminal cases, "a trial court may require a defendant to proceed to trial with counsel not of defendant's choosing." United States v. Oberoi, 547 F.3d 436, 458 (2d Cir.2008) (internal citation and quotation marks omitted). Particularly where, as here, the court has already replaced counsel more than once, and the case approaches trial, it is reasonable for the court to require an intractable defendant either to proceed with the current appointed lawyer, or to proceed pro se. See, e.g., United States v. Eltayib, 88 F.3d 157, 168-69 (2d Cir.1996); McKee v. Harris, 649 F.2d 927, 931-32 (2d Cir.1981).

A defendant faced with a choice between retaining his current court-appointed counsel and proceeding pro se is entitled to elect the latter option, because "the Sixth Amendment right to the assistance of counsel implicitly embodies a correlative right to dispense with a lawyer's help." Faretta v. California, 422 U.S. 806, 835, 95 S.Ct. 2525, 45 L.Ed.2d 562 (1975) (internal quotation marks and citation omitted). But this is a choice that the defendant himself must make, and he must be given a full and fair opportunity to consider his options before waiving his Sixth Amendment right in a knowing and voluntary manner. The able and experienced District Judge may well have been right to decline to appoint new counsel. In doing so, however, the District Judge failed to inform Culbertson of the consequences of waiving his rights under the Sixth Amendment and proceeding pro se. Although a district court may, "under certain circumstances, require the defendant to select from a limited set of options a course of conduct regarding his representation," McKee, 649 F.2d at 931, it must "strive for a full and calm discussion with the defendant in order to satisfy itself that he has the requisite capacity to understand and sufficient knowledge to make a rational choice." United States v. Tracy, 12 F.3d 1186, 1192 (2d Cir.1993) (internal quotation marks and citation omitted); see also Torres v. United States, 140 F.3d 392, 401 (2d Cir.1998) ("[T]he district court should engage the defendant in an on-the-record discussion to ensure that she fully understands the ramifications of her decision.").

Thus, a defendant who, wisely or not, seeks to represent himself "should be made aware of the dangers and disadvantages of self-representation, so that the record will establish that he knows what he is doing and his choice is made with eyes open." Faretta, 422 U.S. at 835, 95 S.Ct. 2525 (internal quotation marks and citation omitted). Without resort to any particular "talismanic procedures," a district court should establish that "the defendant understood that he had a choice between proceeding pro se [or] with assigned counsel, . . . understood the advantages of having one trained in the law to represent him, and . . . had the capacity to make an intelligent choice." United States v. Hurtado, 47 F.3d 577, 583 (2d Cir.1995) (citations and internal quotation marks omitted).

Here, notwithstanding Culbertson's assertions that he was unable to represent himself at trial, the District Court did not apprise him of the consequences of proceeding pro se or assess his capacity to make an informed choice. On remand, if the District Court still finds it appropriate to deny the request for new counsel, Culbertson must be allowed to make his own decision as to whether to proceed pro se or accept his (competent) court-appointed counsel, after a full Faretta hearing. Of course, the District Court retains discretion to appoint new counsel on remand if that is appropriate.

CONCLUSION

For the reasons stated, we REMAND the case to the District Court with instructions to vacate the judgment of conviction and for further proceedings not inconsistent with this opinion.